ACTA TECHNICA NAPOCENSIS

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1 897 TECHNICAL UNIVERSITY OF CLUJ-NAPOCA ACTA TECHNICA NAPOCENSIS Series: Applied Mathematics and Mechanics Vol. 55, Issue IV, 2012 MODELING AS FUNCTION OF TEMPERATURE OF VISCOSITY AND DENSITY FOR BLENDS OF DIESEL FUEL AND THERMALLY DEGRADED POLYETHYLENE George Liviu POPESCU Abstract: The paper presents the mathematical modelling of dynamic viscosity, kinematic viscosity and density as a function of temperature for a series of binary blends between the commercial diesel fuel () and a fuel obtained by thermal degradation of Low Density Polyethylene (LDPE). The values for viscosities and density were calculated starting from the measured values for and LDPE fuel as a function of temperature. The Gas Chromatography coupled with Mass Spectroscopy (GC-MS) has been used for the determination of the composition of the fuel obtained by thermal degradation of LDPE. Based on the data obtained by GC-MS the molecular weight of the fuel obtained by pyrolysis of LDPE has been calculated and the mole fraction of each component. Key words: recycling, fuel, modelling, viscosity, density. 1. INTRODUCTION European regulators are setting increasingly stringent standards to reduce the impact of waste plastic materials (PM) on the environment. These regulations include the Directives 94/62/EC and 2005/20/EC on Waste Packaging (Romanian Government Decisions no. 349/2002 and 899/2004), the Directive 2000/53/CE on End of Life Vehicles (ELV) (Romanian Government Decision no. 2406/2004) and the Directive 2002/96/CE on Waste Electrical and Electronic Equipment [1]. Recent statistics for Western Europe estimate the annual consumption of plastic products at almost 100 kg/person for a total of over 39.1 million tons [1, 2]. This generates a vast waste stream, estimated at around 21.5 million tons/year, that needs to be effectively managed. Large quantities of all the waste plastics from Europe are still disposed of to landfill. In Romania a small quantity of plastic waste are recovered and recycling. Plastic material generates serious environmental problems due to their low density and high volume, resistance to biological degradation and combustible nature. This is the reason for intensive research for searching new and efficient methods for plastic materials recycling. Among recycling methods, tertiary recycling leads to total depolymerization to monomers, or partial degradation to other secondary valuable materials [3] such as fuels or raw materials such as lubricating oils, synthesis gas [4]. Polyolefines contains chains formed only from carbon and hydrogen, being the most important candidates for chemical recycling for the obtaining of fuels [5]. Other plastic materials form corrosive or toxic degradation products when heated for recycling. Polyvinyl chloride (PVC) evolves corrosive hydrochloric acid (HCl) during thermal treatments applied for chemical recycling trough pyrolysis [6-9]. Polystyrene degradation conducted to a high concentration of toxic styrene. Other PM can form very toxic halogen or nitrogen containing organic compounds during tertiary recycling. Even if the obtaining of fuels starting from polymers waste was intensively studied, research related to the properties of binary mixtures formed from diesel fuel and fuels

2 898 obtained by plastic materials recycling were not approaches. The paper presents a study related to mathematical modelling of dynamic viscosity, kinematic viscosity and density of different blends of commercial diesel fuel and LDPE derived fuel starting from the measured properties of and LDPE fuels as a function of temperature. 2. EXPERIMENTAL 2.1 The obtaining of LDPE pyrolysis fuel A bench scale installation has been used for the obtaining of fuel starting from LDPE waste. The installation is formed from a heated reactor, a cooling unit and a system for the collection of the reaction products. Gas chromatography coupled with mass spectroscopy has been used for liquid phase analysis using a GC-MS system Agilent 7890A. The density the dynamic and kinematic viscosity of the fuel obtained from LDPE and commercial diesel fuel (EN ) has been determined using SVM 3000 Stabinger Viscometer (Anton Paar), at a pressure of 974 [mbar] and a temperature of 27.6 o C, according to ASTM D7042. The results were presented according to ISO 3104 or ASTM D The characterization of the blends of LDPE pyrolysis fuel and diesel fuel The molecular weight of the LDPE derived fuel was calculated based on GC-MS results with the relation: M = ν i M i (1) where: ν i is the molar fraction of each identified compound and M i is the molecular weight. The molar fractions of the compounds (ν i ) from the oil obtained through pyrolysis have been obtained with the relation: n i ν i = (2) n where: n i is the numbers of moles of the compound i from the mixture and n is the total number of moles. Based on the molecular weight of the diesel fuel (230 g/mole), the calculated molecular weight of LDPE oil (208 g/mole), the density (ρ) of the fuels at 20 o C and the volumes (V) used for blends preparation, the numbers of the moles (N) from the mixture were calculated with the relation: N N = ( ρ V )/ M (3) LDPE _ F ( LDPE _ F VLDPE _ F )/ = ρ M (4) LDPE _ F Using the numbers of the moles (N) of the two fuels from the blend, the variation of: dynamic viscosity, cinematic viscosity and density as a function of temperature for the obtained mixture has been calculated with the relations: Kinematic viscosity: ν = ν N + ν N (5) c d () t ( ) c() t, LDPE _ F LDPE _ F c t, Dynamic viscosity: ν = ν N + ν N (6) () t d () t d () t, LDPE _ F LDPE _ F Density:, ρ = ρ N + ρ N (7) () t () t () t, LDPE _ F LDPE _ F, tacking into account the values obtained for the pure commercial diesel fuel and the fuel obtained from LDPE (LDPE_F). We took into consideration a series of blends, containing LDPE_F in a concentration of 5, 10, 25, 50, 70 volume % into diesel fuel. 3. RESULTS AND DISCUSSION 3.1 GC-MS analysis Figure 1 presents the chromatogram of the low density polyethylene derived fuel and table 1 the results of chromatogram interpretation. The obtained fuel contains saturated and unsaturated hydrocarbons with carbon numbers from 8 to 25. One can see from table 1 that the unsaturated compounds are in smaller quantities comparing to saturated compounds. As can be seen in table 1, no aromatic compounds were identified in

3 899 LDPE fuel, leading to the conclusion that using these fuels the quantity of toxic polycyclic aromatic hydrocarbons will decrease. Table 1 The composition, mole number and molar fraction of LDPE derived fuel determined by GC-MS Assignment Area % Moles Molar fraction 1-Octene Octane Nonene Nonane Decene Decane Undecene Undecane Dodecene Dodecane Tridecene Tridecane Tetradecene Tetradecane Pentadecene Pentadecane Hexadecene Hexadecane Heptadecene Heptadecane Octadecene Octadecane Nonadecene Nonadecane Eicosene Eicosane Heneicosane Docosane Tricosane Tetracosane Pentacosane Fuels blends properties modelling Starting from the calculated mole fractions (table 1) and the measured dynamic viscosity ν d, kinematic viscosity ν c and density ρ respectively as a function of temperature for commercial diesel fuel and low density polyethylene derived fuel, the dynamic viscosity, kinematic viscosity and density for a series of commercial diesel fuel and low density polyethylene derived fuel blends has been calculated. The values resulted from calculations as a function of temperature have been fitted using polynomial regression for viscosity, and linear regression for density. The dependence of measured dynamic viscosity for commercial diesel fuel and low density polyethylene derived fuel are presented in fig. 3. The dependence of dynamic viscosity as a function of temperature fit polynomial equation of third grade (table 2). The dependence on temperature of the calculated values for dynamic viscosity of the blends are also presented in fig. 2. One can observe that the variation of calculated dynamic viscosity on temperature fit also third grade polynomial equations. The resulted equations ν d = f(t) and the correlation factor (R 2 ) for the polynomial regressions are presented in table 2. Examining table 2 and figure 2 one can see that the calculated values for dynamic viscosity in the case of the blends from commercial diesel fuel and low density polyethylene derived fuel are between the values of pure diesel fuel and low density polyethylene derived fuel. We also observe a very high value of the correlations factors (R 2 > 0.997) for all equations. The viscosity of the fuel obtained from LDPE is smaller than the viscosity of commercial diesel fuel and all the blends have intermediate values. Abundance Time--> TIC: combustibil_plastic.d\data.m Fig. 1. Chromatogram of LDPE_F fuel

4 900 Fig. 2. The variation of dynamic viscosity on the temperature for blends formed from diesel fuel and LDPE derived fuel (measured for pure fuels and calculated for blends) Table 2 Polynomial equations of the variation of the dynamic viscosity as a function of temperature Fuel Equation R 2 Commercial y = -1E-05x x diesel fuel x % LDPE y = -1E-05x x x % LDPE y = -9E-06x x x % LDPE y = -8E-06x x x % LDPE y = -7E-06x x x % LDPE y = -6E-06x x x % LDPE y = -4E-06x x x Similar conclusions can be drawn for kinematic viscosity. The kinematic viscosity of low density polyethylene derived fuel is smaller than the value of commercial diesel fuel. The calculated values for the blends are intermediate between the values for commercial diesel fuel and low density polyethylene Fig. 3. The variation of kinematic viscosity on the temperature for blends formed from diesel fuel and LDPE derived fuel (measured for pure fuels and calculated for blends) Table 3 Polynomial equations of the variation of the kinematic viscosity as a function of temperature Fuel Equation R 2 Commercial y = -1E-05x x diesel fuel x % LDPE y = -1E-05x x x % LDPE y = -1E-05x x x % LDPE y = -1E-05x x x % LDPE y = -8E-06x x x % LDPE y = -7E-06x x x % LDPE y = -4E-06x x x derived fuel (fig. 3 and table 3). The equations for ν c = f(t) fit third grade polynomial regressions. The resulted equations and the values obtained for the correlation coefficient R 2 are presented in table 3.

5 901 Very high values for correlation coefficient (R 2 > 0.997) can be observed from table 3 for all equations. Density exhibits a linear variation as a function of the temperature (figure 4). The slope of the curves is for all samples except sample containing 70 % low density polyethylene derived fuel which is The intercept for the linear equations decreases with the increasing of the amount of low density polyethylene derived fuel in the blends. The correlation factor is 1 for all curves ρ = f(t). One can also notice that the density of low density polyethylene derived fuel is smaller than the density of commercial diesel fuel and their blends. Fig. 4. The variation of density on the temperature for blends formed from diesel fuel and LDPE derived fuel (measured for pure fuels and calculated for blends) Table 4 Linear equations of the variation of the density as a function of temperature Fuel Equation R 2 y = x % LDPE y = x % LDPE y = x % LDPE y = x % LDPE y = x % LDPE y = x % LDPE y = x The calculated values of dynamic viscosity, cinematic viscosity and density correspond to standards, leading to the conclusion that a wide range of blends could be used in internal engines. Low density polyethylene derived fuel can be a good candidate for using in blends with commercial diesel fuels. 4. CONCLUSION The paper presents the mathematical modelling of dynamic viscosity, kinematic viscosity and density as a function of temperature for a series of binary blends of commercial diesel fuel () and a fuel obtained by thermal degradation of Low Density Polyethylene (LDPE). The values for viscosity and density were calculated starting from the measured values for and LDPE fuel as a function of temperature. Based on the data obtained by Gas Chromatography coupled with Mass Spectroscopy, the molecular weight of the fuel obtained by pyrolysis of LDPE and the mole fraction of each component has been calculated. We concluded that the blends formed from and LDPE fuel can be used in compression ignition engine and the studied properties (kinematic viscosity, dynamic viscosity and density) meets the demands imposed by actual legislation. AKNOWLEDGEMENT This paper was supported by the: Ministry of Education, Research, Youth and Sports by the project "Proiect de dezvoltare a studiilor de doctorat în tehnologii avansate - PRODOC contract no. POSDRU/6/1/5/S/5, project co-funded from European Social Funds through Sectorial Operational Program Human Resources Author thanks to Assoc. Prof. PhD. Eng. Istvan Barabas for viscosity and density measurements and to Researcher PhD. Eng. Adriana Gog for GC-MS analysis.

6 REFERENCES [1] Aguado J., Serrano D.P., San Miguel G., European trends in the feedstock recycling of plastic wastes, Global NEST Journal, [2] Association of Plastic Manufacturers in Europe (APME), An analysis of plastics consumption and recovery in Europe , Brussels (Belgium) [3] Achilias D.S., Roupakias C., Megaloko-nomos P., Lappas A.A., Antonakou E.V., Chemical recycling of plastic wastes made from polyethylene (LDPE and HDPE) and polypropylene (PP), Journal of Hazardous Materials, 149 (2007) [4] Mastral J.F., Berrueco C., Ceamanos J.. Theoretical prediction of product distribution of the pyrolysis of high density polyethylene. Journal of Analytical Applied Pyrolysis, [5] Piétrasanta Y., Livre blanc sur le recyclage des matières plastiques, Les impressions Dumas, 42100, Saint Etienes [6] Miskolczi N., Bartha L., Angyal A., Pyrolysis of Polyvinyl Chloride (PVC)-Containing Mixed Plastic Wastes for Recovery of Hydrocarbons, Energy Fuels, [7] Ma S., Lu J., Gao J., Study of the Low Temperature Pyrolysis of PVC, Energy Fuels, [8] Grause G., Buekens A., Sakata Y., Okuwaki A., Yoshioka T., Feedstock recycling of waste polymeric material, Journal of Material Cycles and Waste Management, [9] Kameda T., Imai K., Grause G., Mizoguchi T., Yoshioka T, Kinetics of the dehydrochlorination of poly(vinyl chloride) in the presence of NaOH and various diols as solvents, Polymers Degradation and Stability, Modelarea în funcţie de temperatură a viscozităţii şi densităţii mixturilor motorinei cu polietilena degradată termic Rezumat: Lucrarea prezintă modelarea matematică a viscozităţii dinamice, viscozităţii cinematice şi a densităţii în funcţie de temperatură, pentru o serie de amestecuri binare formate din motorina comercială () şi un combustibil obţinut prin degradarea termică a Polietilenei de Joasă Densitate (LDPE). Valorile pentru densitate şi viscozităţi au fost calculate pornind de la valorile măsurate pentru şi combustibilul derivat din LDPE în funcţie de temperatură. S-a utilizat Cromatografia de Gaze cuplată cu Spectroscopia de masă (GC_MS) pentru determinarea compoziţiei combustibilului format în urma degradării termice a LDPE. Pe baza datelor obţinute prin GC-MS s-a calculat masa moleculară a combustibilului obţinut prin piroliza LDPE şi fracţiile molare ale fiecărui component. George Liviu POPESCU, PhD student, Eng. Technical University of Cluj-Napoca, Department of Automotive and Transportation, georgepopescu60@gmail.com Tel: (+)